Physical relationships and Time

It has been proposed that all relative measures of time slow with the expansion of spacetime. This will be verified for the following physical processes.
1. A light Clock
2. A pendulum
3. A spinning planet or object
4. An orbiting planet or object


The Ratios of Time
(Capitol letters indicate “absolute measures”, 1 and 2 are earlier and later measures respectively)
D1/D2 == (T1/T2)^(2/3)
V2/V1 == (T1/T2)^(1/3)
A2/A1 == (T1/T2)^(4/3)
E2/E1 == (T1/T2)^(2/3) [/b]

The light clock,
Based upon absolute measures, the speed of light slows and the distance the photon must travel increases with the expansion of spacetime. This means that based upon absolute measures it is going to take a photon longer to travel back and forth between two mirrors. Locally there should be no indication of the change, which requires all physical measures of time (except nuclear decay rates) to all slow down the same proportional amount. Sounds impossible, but it is actually amazing.

First off, the change in distance is not observed since proportionally everything else proportionally expands. This leaves the challenge of checking that all measures of relative time also stay the same.

Using the Ratio of time formula describing how the distance the photon travels will vary, we have
D1/D2 == (T1/T2)^(2/3)
If the age of the universe were to double, the corresponding increase in absolute distance is
D2/D1 == (T2/T1)^(2/3) = 2^(2/3) = 1.59… The light clock is longer by this proportion.

Note that since the age of the universe is billions of years old, and the ratios of time formulas use this measure of time as a basis for describing relationships, events over a few thousand years represent a small, almost insignificant change.

Using the Ratio of time formula describing how the speed of a photon changes with the expansion of spacetime,
V2/V1 == (T1/T2)^(1/3)
If the age of the universe were to double, the corresponding decrease in the absolute velocity of the photon is
V2/V1 == (T1/T2)^(1/3) = (1/2)^ (1/3) = .79….

In the case where the age of the universe doubles, it would take the photon D/V = 1.59/.79 = 2 times longer to describe a cycle.

Generally the relationship is
D/V = interval of time = D2/D1 / V2/V1 = (T2/T1)^(2/3) / (T1/T2)^(1/3) = T2/T1. Double the age of the universe and the interval of time described by a light clock doubles.

A pendulum
The Period of a pendulum is = 2 pi x (l/g)^(1/2).

The length of the pendulum changes with the expansion of space-time. The locally experienced acceleration is also effected since the centroidal distance is increased with expansion. Rather than use the increased centroidal distance to reduce the effect of gravity, which would be used for g, the change in accelerative field predicted by the ratio of time formula, A2/A1 = (T1/T2) ^(4/3) will be used. The result is the same but I am trying to show the universality of the relationships.
D2/D1 = (T2 /T1) ^ (2/3)
A2/A1 = (T1/T2) ^(4/3)

The Delta T interval of time for pendulum = change in l/g = (D1/D2/ A1/A2 )^(1/2)
T∆2/T∆1=( D2/D1/ A2/A1)^(1/2) = ((T2 /T1) ^ (2/3) / (T1/T2) ^(4/3))^(1/2) = T2/T1
Double the age of the universe and the interval of time described by a pendulum doubles.

A rotating object
Now lets see if a rotating object also takes twice as long to spin if the age of the universe were to double.

The distance the rotating object must travel increases since the object is expanded. For example if the age of the universe were to double, the size of the object increases 1.59 … times, which means all points rotating on the mass must travel 1.59 times further.

The velocity of any point on the rotating mass must, according to absolute measures, slow down. If the age of the universe were to double the corresponding decrease in the velocity of all the points on the rotating mass would be .79… times.

This is the same form or relationship observed in the light clock, so, so far relative measures have been preserved. Double the age of the universe and the object takes twice as long to spin.

An orbiting object
Now lets see if an orbiting object also takes twice as long to orbit if the age of the universe were to double.
Again, if the age of the universe were to double the distance the orbiting objects must travel increases 1.59… times.

The velocity also slows .79 times and again the overall increase in the time it would take for the planet to orbit the sun would double if the age of the universe were to double. Double the age of the universe and the object takes twice as long to complete an orbit.

Chemical and Biological reactions
Since the electron conforms to the same inverse square law relationships in “orbit” around the atom (Orbit is in quotations indicating a somewhat simplified statement), the same temporal effects would be expected for atomic or chemical reactions. Some may quickly note that a potential problem arises here, potentially destroying the proportional relationships. This is because electrons move at relativistic speeds. However, the gamma “correction” factor used to “adjust” for the relativistic effect keeps the same proportional relationships since the V/C term in “gamma”, (which is the velocity of the electron / the speed of light) is proportionally preserved. So when the universe was 1/2 its present age, even chemical reactions transpired twice as fast. An organism lived twice as fast, did twice as much and died in half the time, compared to today’s organisms. This “speeds” up the evolutionary process. Double the age of the Universe and physical process take twice as long to occur.

Nuclear Decay Rates
Nuclear decay may be an exception to the proportional variation in clock rates. The spatial separation and conformance to the inverse square laws has no obvious correlation to the relationships within the nucleus. Since astronomical evidence indicates that decay rates observed in radioactive material left from supernovas correlates somewhat well to observed historical locations, it is tempting to assume that the effects of an expanding spacetime field stop at the boundary of a nucleus, thereby resolving the issue as to where to stop the expansion of spacetime. http://www.talkorigins.org/indexcc/CF/CF210.html If this is the case, then measures of time based on radioactive decay correlate to absolute measures of time and not relative measures of time.


Comparing Experiential and Absolute Time

(Class is shown a graph of T∆2/T∆1 = T2/T1 which shows how intervals of time verses the historical location is a hyperbolic relationship. )

Near the beginning of time, T1, clock rates are very vast, approaching an infinite rate. What we presently perceive as 1 second now would have represented far more passage of time.

Sample problem
When the universe was 1 year old in Absolute or Historical time, how much more quickly did time pass? Assume a 10 billion year old universe.
T∆2/T∆1 = T2/T1
T∆2/T∆1 = 10,000,000,000/1
T∆1 = T∆2 *1/10,000,000,000

What would corresponds to a process that takes 1 second today would only take 1 ten billionth of a second to happen when the universe was 1 year old, assuming we are using our present measure of time as the “absolute” standard of comparison. Everything would be evolving 10 billion times more quickly. In order to determine the cumulative measure of this experiential time requires taking the integral of the relationship.

Cumulative or experiential time elapsed = te =
= To times (Integral of (1/T) dT , from now(To) to T1, =
= To(ln(To/T1)

Sample problem,
How much experiential time has passed from when the universe was 1 billion years old in absolute or historical time to the present? Assume a 10 billion year old universe.

te = To ln(To/T1)
= 10 ln(10/1) = 23 billion years.

Now when we look back into deep space we are looking back in a measure of time that is Absolute or historical. An object observed when the universe was 1 billion years old, in a 10 billion year old universe, is seen as it was 10 –1, or 9 billion absolute years back in the past. The amount of experiential time that has elapsed while the light from that object located when the universe was 1 billion absolute years old to the present is not 9 billion years, but 23 billion years.

As you can see on this graph, as one approaches the beginning of absolute time, the amount of experiential time approaches infinity. The universe is essentially becoming infinitely old.

Now I have not shown how looking back into space corresponds to absolute time. The following explanation should help.

(Class is shown a figure of a string of evenly spaced light clocks separated by evenly spaced distances. )

Using our Eye of God perspective we can see that all the clocks are separated an equal interval of time from each other. Lets say that at T1 the light clocks are all 1 second away from each other, so at T1, the far end of the string of light clocks is 8 seconds away from the observer.

Now by the time the light reaches the observer it will be T2. But notice this, each light clock, even though it is slowing down with the expansion of spacetime, will still preserve the same local measure of time between each of the points. Each point perceives or measures that they are 1 second away from each other. That perception or measure of time will be preserved as the light from the distant source travels to the observer.

This means that the 8-second separation is preserved, but it is the measure of separation at T1, when the signal was sent. The 8-second measure is the absolute or historical separation between the points.

In the time that it took for the light to travel from the source to the observer, more than 8 seconds of experiential time have actually passed. This is because when the signal was initially sent, clock rates were faster, as shown earlier.

So when we look back into deep space we are looking back in Absolute measures of time, not relative measures of time.


A universe with a beginning and an end
A universe with NO beginning and NO end

This description of the universe using two measures of time is surprising. From our Eye of God perspective, the universe had a beginning and eventually it will end. Based on our relative measures of time, the universe is infinitely aged. It also will never end.

Continued.

Next post, orbital stability and the inverse square laws.